Based On Bayesian Extremum Estimation Of Geological Disaster Loss Distribution And The Study Of Risk Measurement

Extreme value theory is an important subject of statistics theory,specifically was used to study the situation that low frequency high loss events occuring. Since the extreme value theory, it has been widely applied to many fields of study, solved many technical difficult problem.In recent years, the extreme value theory research is becoming more and more associated with people’s life actually, study is becoming more and more extensive. Especially in the financial sector, because of its unique advantages of this kind of event study, extreme value theory produces a great many of related research results. However extreme value theory is rarely involved in the application research of the geological disasters such as floods, landslides, soil erosion debris flow, collapse, collapse and ground subsidence, but this kind of event of small probability events often will bring disastrous consequences. Especially in recent years, due to the influence of human activities, geological disasters occur frequently,causing heavy economic losses. Therefore using the extremum theory to study geological disasters further that has very important practical significance.Extreme value theory mainly includes two kinds of parameter model:the excess extremum model and the interval extremum model. Theinterval extremum model mainly model on the maximum range and it can be used to analyze the occurrence rules of the maximum of interval(such as a year, quarterly, monthly); The excess extremum model mainly set a threshold value and moldel on all more than a given threshold of observation samples. The key to the two model can be builded is threshold determination and estimation of parameter, in this paper, the two key problems also carried on the thorough and focus of research. In view of the low frequency high damage characteristics of extreme events,the lack of datas tends to lead to the parameter estimation results credibility is not high. So based on the extremum theory, in this paper,and using the bayesian estimation method to estimate the parameters of the two excess extremum model, so it can minimize error that is too large under the condition of insufficient extremum data, brought by the method of maximum likelihood estimation.This article follows the research thought from theory research to the empirical analysis and main contents include three parts:The first part is the extremum model and Bayes estimation theory presentation. Mainly introduces the generalized Pareto distribution, limit theorem and GPD model, all the Paretian extremum model and the Bayes estimation theory.The second part is on the building of the disaster distribution model and risk measurement. Mainly introduces two methods of fat-taileddistribution test, three kinds of method to determine the threshold value,the parameter estimation of three kinds of methods, as well as several estimation methods of risk measurement. This part is very important to model accurately build.The third part is the empirical research based on the excess model and bayes estimation. Mainly uses the sample data to model, and through parameters test to establish the optimal model,also makes the risk measurement to model. The empirical results also show that the bayesian extremum model is of great significance on the study of geological disasters.